Simplify the following expression: $p = \dfrac{y^2 + 16y + 63}{y + 9} $
Solution: First factor the polynomial in the numerator. $ y^2 + 16y + 63 = (y + 9)(y + 7) $ So we can rewrite the expression as: $p = \dfrac{(y + 9)(y + 7)}{y + 9} $ We can divide the numerator and denominator by $(y + 9)$ on condition that $y \neq -9$ Therefore $p = y + 7; y \neq -9$